Abstract
We give simple proofs that a weak solution u of the Navier–Stokes equations with H 1 initial data remains strong on the time interval [0, T] if it satisfies the Prodi–Serrin type condition u ∈ L s(0, T;L r,∞(Ω)) or if its L s,∞(0, T;L r,∞(Ω)) norm is sufficiently small, where 3 < r ≤ ∞ and (3/r) + (2/s) = 1.
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Communicated by R. Shvydkoy
JCR is supported by an EPSRC Leadership Fellowship EP/G007470/1.
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Bosia, S., Pata, V. & Robinson, J.C. A Weak-L p Prodi–Serrin Type Regularity Criterion for the Navier–Stokes Equations. J. Math. Fluid Mech. 16, 721–725 (2014). https://doi.org/10.1007/s00021-014-0182-5
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DOI: https://doi.org/10.1007/s00021-014-0182-5